According to [1]} we can infer from Proposition REF  that the magnetic spectral triple \(({S}_B,{H}_4,D_B)\)  is \(p\) -summable
for every \(p>4\)  and \(4^+\) -summable. In particular this would imply that
its classical dimension is 4.
However, it is worth recalling that \({C}_B\)  (and hence \({S}_B\) ) is not unital and therefore, a more appropriate definition of dimension is given by [2]}.
Let us also observe that the operator \(|D_{B,\varepsilon }|\)  and the Dixmier trace can be combined to compute the trace \(_B\)  of the von Neumann algebra \({M}_B\) . Indeed, as a direct consequence of Proposition REF 
one gets for all \(T\in {L}^1_B\) 

B(T) = 14TrDix(|DB,|-2(T))
= 14TrDix((T)|DB,|-2)
